OK, I just put the USB/AUX module back in the truck and hooked it back up to it's stock harness. That fixed the "AUX input not being presented in the stock headunit's Audio Source menu" issue. Now music works in Android Auto. However, phone calls now aren't working through the new mic. I've got the phone paired through the NetPlay unit, but during a phone call, Android Auto says "Bluetooth is not connected". At this point, I'm not sure what to do. I've emailed NaviPlus.
EDIT: It should be noted that the PAC USB-TY2 adapter does not fit into the stock USB/AUX module. My original intention was to plug the NaviPlus supplied female USB type A into the PAC adapter's USB Type A male and then the Toyota USB side of that PAC adapter into the USB/AUX module. That PAC adapter does not fit into the stock USB/AUX module, which is what led me to remove it which then led to my "No AUX Input Listed in Menu" issue. For now, I have that female USB Type A plug hanging out by the passenger's feet until I can figure out the proper install method. I also don't think this will fast charge my phone. During a 10 minute trip yesterday, the phone didn't lose charge, but it didn't gain any either.